The Spanish world number five drove behind the trees at the last but produced a lofted approach to just two feet for a round of six-under 65 and a halfway 11-under 131 total.
By contrast Finch (66) and overnight leader Kjeldsen (67) bogeyed the final hole after Garcia's wonder shot to leave the trio two strokes clear.
"I've played that shot a lot of times but it's the first time it's come out that close and it made it a little more special by doing it under pressure," Garcia said.
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While course knowledge on his revamped layout is working to the Spaniard's favour in the inaugural event, the pressure to deliver remains high.
"It's a special week in front of my own crowd, so there is a little bit of pressure to do well. Hopefully I'll be 100 per cent at the weekend, I'm looking forward to it."
Garcia needed to find something special after watching his playing-partner and house guest Camilo Villegas hit a hole-in-one on the 12th on his way to a 66 to lie at six-under-par in the chasing pack.
Colombian world number seven Villegas, playing thanks to an invitation from Garcia, aced with a five-iron from 217 yards.
"I told him 'you're not supposed to do those things on my home course when I am hosting you'," Garcia joked.
"But it was amazing. It's the hole where I had my very first hole-in-one and it's his first hole in one as a professional."
Garcia, recently beaten by Villegas in a playoff for the US Tour Championship, is aiming for his first European Tour win since claiming the 2005 European Masters title - when he beat then house guest, Luke Donald, down the closing stretch.
Despite their closing mishaps, Finch, who this time last year was desperately trying to retain his Tour card, and Kjeldsen may spoil Garcia's weekend while the five players tied on nine-under in fourth place have reasons for strong finishes.
Spaniard Alvaro Quiros (66) is gunning for successive titles after winning last week in Portugal. Britain's Simon Dyson (67) and David Lynn (66) and Swede Peter Hedblom (65) are jockeying for starts in next week's Volvo Masters.
Frenchman Francois Delamontagne (67) sits 119th on the European money list, just one place away from ensuring his playing card for 2009.
Swede Patrik Sjoland, lying in the 118th and final exempt spot for next season, missed the cut and will now have to hope he is not overtaken at the weekend.
U.S. Open
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